In a system for the communication and/or storage of signals representing, for example, speech, image or video information, the signals to be transmitted or stored are often coded or compressed to reduce the amount of data required to represent them. One technique useful for achieving such signal compression while maintaining signal quality of the subsequently decoded signal is subband coding. In subband coding the frequency spectrum of the signal to be coded is divided into a plurality of subbands by a bank of bandpass filters (the analysis filter bank). Each subband is, in effect, translated to zero frequency by modulation techniques, and then sampled (or resampled) at its Nyquist rate (twice the width of the band). Each individual subband signal is then digitally encoded, typically by a quantizer with a preselected number of quantization levels.
On reconstruction, the encoded subband signals are decoded and translated back to their original locations in the spectrum. These reconstructed subband signals are then combined using synthesis filters to give a close replica of the original signal. With this technique, each subband can be encoded according to criteria (including perceptual criteria) that are specific to that band. In particular, the number of bits per sample (dependent on the number of quantizer levels) in each band can be individually allocated, thereby separately controlling the reconstruction error variance in each band. In this way, the inherent tradeoff between bits per sample and reconstructed signal quality can be optimized based on the characteristics of the type of input signal. For example, in the case of speech signals, a relatively larger number of bits per sample are typically used in the low to medium frequency bands, where pitch and formant structure are advantageously preserved for faithful reproduction of the signal.
The principals of subband coding techniques are described generally in N. S. Jayant and P. Noll, Digital Coding of Waveforms: Principles and Applications to Speech and Video, ch. 11, Prentice-Hall, Englewood Cliffs N.J., 1984, and in Subband Image Coding (J. W. Woods, ed.), ch. 2, Kluwer Academic Publishers, Boston Mass., 1991, each of which is hereby incorporated by reference. In addition, aspects of the use of subband coding techniques to reduce bitrates for digital speech communication are described in detail in U.S. Pat. No. 4,048,443, issued on Sep. 13, 1977, to R. E. Crochiere et al., and assigned to the assignee of the present invention. The Crochiere patent is also hereby incorporated by reference. The application of subband coding techniques to still images and to video signals are described, e.g., in Subband Image Coding.
Much of the work on subband coding techniques has been directed to reconstructing the original signal from individual subband signals. Specifically, such work has emphasized recreating as closely as possible the original (unquantized) input signal, while ignoring any loss of information due to coding (quantization) effects. It is well known that the bandpass filters used in the analysis filter bank can never have perfectly sharp cut-offs (as do "brick wall" filters). Thus, one effect of dividing the original signal into subbands and subsequently recombining the subbands is to produce errors relating from signals from other subbands. The effect of these errors should be reduced or eliminated by the synthesis filters used to process the subband signals.
Early efforts in this direction addressed the aliasing effects which occur when overlapping subbands are sampled at a frequency less than twice the entire width of the band (including all of the corresponding analysis filter's roll-off). One result of these efforts was the Quadrature Mirror Filter (QMF) technique, described, e.g., in Jayant and Noll, ch. 11. Using QMF techniques, aliasing effects resulting from the reconstruction of the original signal from its overlapping subbands may be entirely eliminated by synthesis filters having transfer functions based on the transfer functions of the analysis filters. In other efforts, so-called perfect reconstruction filter sets have been developed in which the original (unquantized) input signal can be replicated perfectly in the absence of coding errors based on appropriate synthesis filters. Again, this is accomplished by using synthesis filters having transfer functions based on the transfer functions of the analysis filters.
Given this state of the art, a typical approach used by designers of subband coding systems is to use a perfect reconstruction (or alias-cancellation QMF) filter bank and then to select subband quantizers. However, the selection of the quantizers has not been an integral part of the design of the filter banks. As used in this discussion, overall (total) reconstruction error is determined as the difference between the input signal applied to the analysis filter bank and the resultant output (replica) signal produced by combining the outputs of the synthesis filters. Since the quantization error cannot be eliminated by the design of the filters (a quantization by its nature results in a loss of information), prior subband coding systems have sought to achieve minimum overall reconstruction error using perfect reconstruction filter banks and separately optimized (minimal loss) quantizers. Moreover, such optimal, minimum error quantizers, so-called Lloyd-Max quantizers, are well known in the art.